High performance tires used for sports cars, racing cars and the like are required that the grip force at low temperatures be high and further that the decrease in performance at the time of the repeated use in circuit driving and the like be small. Namely, it is important to exhibit a high grip force from the onset of driving and to maintain the performance after the generation of large heat in the tire during driving. From such viewpoints, the present inventors previously developed a rubber composition capable of improving the grip force of a tire, without impairing the blowout resistance (see Japanese Patent Publication (A) No. 10-204216). However, in the industry, further needs are still existed.